A Note on the Shapley Value for Characteristic Functions on Bipartitions

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We consider a cooperative game with a bipartition that indicates which players are participating. This paper provides an analytical solution for the Shapley value when the worth of a coalition only depends on the number of participating coalition players. The computational complexity grows linearly in the number of players, which contrasts with the usual exponential increase. Our result remains true when we introduce (i) randomization of the bipartition, and (ii) randomly draw a characteristic function.
Original languageEnglish
Place of PublicationDen Haag
PublisherCPB Netherlands Bureau for Economic Policy Analysis
Number of pages12
Publication statusPublished - 28 Aug 2011
Externally publishedYes

Publication series

NameCPB Discussion Paper


  • Shapley value
  • computational complexity
  • bipartition


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